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arXiv · 1205.2852

\epsilon-regularity for systems involving non-local, antisymmetric operators

Armin Schikorra
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Abstract

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivi\`ere treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivi\`ere. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations.

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Armin Schikorra. 2012-05-13. \epsilon-regularity for systems involving non-local, antisymmetric operators. https://doi.org/10.1007/s00526-015-0913-3

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